Closed and noise-tolerant patterns in n-ary relations

Cerf, Loïc; Besson, J.; Nguyen, Kim-Ngan T.; Boulicaut, Jean-François

doi:10.1007/s10618-012-0284-8

Cited by 44 publications

(52 citation statements)

References 31 publications

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“…Analogously, we can consider Boolean CP tensor decomposition as an N -way lossy tiling, generalizing the N -way tiling [9]. Again, finding the least number of tiles needed to express the data set exactly is equivalent to finding the Boolean tensor rank, and minimizing the number of uncovered 1s in N -way tiling is related to minimizing the error in Boolean CP tensor decomposition (with the latter allowing the covering of 0s with 1s).…”

Section: Relations To Other Data Mining Methodsmentioning

confidence: 99%

Boolean Tensor Factorizations

Miettinen

2011

2011 IEEE 11th International Conference on Data Mining

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Abstract-Tensors are multi-way generalizations of matrices, and similarly to matrices, they can also be factorized, that is, represented (approximately) as a product of factors. These factors are typicaly either all matrices or a mixture of matrices and tensors. With the widespread adoption of matrix factorization techniques in data mining, also tensor factroziations have started to gain attention.In this paper we study the Boolean tensor factorizations. We assume that the data is binary multi-way data, and we want to factorize it to binary factors using Boolean arithmetic (i.e. defining that 1+1 = 1). Boolean tensor factorizations are, therefore, natural generalization of the Boolean matrix factorizations. We will study the theory of Boolean tensor factorizations and show that at least some of the benefits Boolean matrix factorizations have over normal matrix factorizations carry over to the tensor data. We will also present algorithms for Boolean variations of CP and Tucker decompositions, the two most-common types of tensor factorizations. With experimentation done with synthetic and real-world data, we show that Boolean tensor factorizations are a viable alternative when the data is naturally binary.

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Section: Relations To Other Data Mining Methodsmentioning

confidence: 99%

Boolean Tensor Factorizations

Miettinen

2011

2011 IEEE 11th International Conference on Data Mining

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“…The last paper shows how tiles can be used to understand complex proteins by identifying their subunits. The authors of [4] also showed that the dense rectangles in a binary matrix seem to correspond to interesting concepts. Therefore, mining large tiles may help to identify those interesting concepts from the databases.…”

Section: Related Workmentioning

confidence: 99%

Mining Top-K Largest Tiles in a Data Stream

Lam

Pei

Prado

et al. 2014

Machine Learning and Knowledge Discovery in Databases

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Abstract. Large tiles in a database are itemsets with the largest area which is defined as the itemset frequency in the database multiplied by its size. Mining these large tiles is an important pattern mining problem since tiles with a large area describe a large part of the database. In this paper, we introduce the problem of mining top-k largest tiles in a data stream under the sliding window model. We propose a candidatebased approach which summarizes the data stream and produces the top-k largest tiles efficiently for moderate window size. We also propose an approximation algorithm with theoretical bounds on the error rate to cope with large size windows. In the experiments with two real-life datasets, the approximation algorithm is up to hundred times faster than the candidate-based solution and the baseline algorithms based on the state-of-the-art solutions. We also investigate an application of large tile mining in computer vision and in emerging search topics monitoring.

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“…Based on these algorithms, [6] propose Data Peeler which performs better than the previous ones and generalized to n-ary relations. [18] propose an approach of discovering rules applied to dynamic relational graphs that can be encoded in n-ary relations (n ≥ 3) [19], [5] propose the generalization of the concept of association rule in such a multi-dimensional context. Study directly related to the discovery of association rules in online analytical processing (OLAP) cubes, [14] who introduced the concept of Meta-rule-guided mining based on model rules defined by the users, in order to guide the mining process.…”

Section: State Of the Artmentioning

confidence: 99%